So I've heard that recent observations indicated that the rate of expansion of the universe is accelerating. Does this indicate that the universe can NOT be cyclical, with an infinite series of big bangs and crunches extending forward and backward through time? Does it "prove" that the universe will not crunch?

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The conformal cyclic cosmology Alfred mentioned is an idea from Roger Penrose. An unrelated idea is from Andrei Linde. See for example this paper or Google for more info. To be honest the details are beyond me, but Linde suggests that dark energy can change sign and cause a collapse. This means the universe could be cyclic even though dark energy is currently causing an accelerated expansion.

However, both Penrose's and Linde's ideas are highly speculative, and I suspect most of us believe that dark energy does indeed mean that the universe cannot be cyclic.

I was thinking that the expansion/contraction model of the old school is more likely than the big bang. I have this idea that the electric theory of the universe;not sure where the power comes from but it seems to be time-varying,is more correct than other options. Magnetic field in plasma create pressures not possible on Earth that make a black hole;aka LT starbody.
Over time the LT whose center has become a galactic nucleus loses pressure after it attains weight ratios (galactic nucleus/galaxy) stability, jets infrequently horizontally through the galactic center and not axially, off gassing from these events surrounding the entire galaxy with a gas cloud that cools and becomes a starless dark. Cold gas clouds then become the majority of the universe dark energy;expansion allowing further cooling which then reaches $0K$ and phase changes.
here:https://www.llnl.gov/str/Schneider.html